Equity Premium in India

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The Equity Premium in India

Rajnish Mehra

University of California, Santa Barbara

andNational Bureau of Economic Research

January 06

Prepared for the Oxford Companion to Economics in Indiaedited by Kaushik Basu


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The equity premiumis the return earned by a risky security, such as a stock, in

excessof that earned by a risk free security, such as a Treasury Bill. It is a crucial input

into financial decisions such as asset allocation, capital budgeting and planning for

retirement.

Historical data provide a wealth of evidence documenting that over long periods

of time, stock returns have been considerably higher than returns for T-bills. As Table 1

shows, the average annual real return (that is, the inflation-adjusted return) on the U.S.

stock market for the past 115 years has been about 7.5 percent. In the same period, the

real return on a relatively riskless security was a paltry 1.0 percent.

Table 1.

U.S. Returns, 18022004Mean Real Return

Period Market Index

Relatively

Riskless

Security Risk Premium

18022004 6.9% 2.9% 4.0%

18892004 7.5 1.0 6.5

19262004 8.0 0.7 7.3

19472000 7.5 0.5 7.0

The difference between these two returns, 6.5 percentage points, is theequity

premium. This statistical difference has been even more pronounced in the post-World

War II period. Data on U.S. stock and bond returns going back to 1802 reveal a similar,

although somewhat smaller, premium for the past 200 years.


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Furthermore, this pattern of excess returns to equity holdings is not unique to

U.S. capital markets. Table 2 documents that equity returns in other developed

countries also exhibit this historical regularity when compared with the return to

riskless debt holdings.

Table 2

Returns for Selected Developed CountriesMean Real Return

Country Period Market Index

RelativelyRiskless

Security

Risk

Premium

United Kingdom 19471999 5.7% 1.1% 4.6%

Japan 19701999 4.7 1.4 3.3

Germany 19781997 9.8 3.2 6.6

France 19731998 9.0 2.7 6.3

Sweden 1919-2003 11.1 5.6 5.5Australia 1900-2000 13.3 4.6 8.7

The annual return on the U.K. stock market, for example, was 5.7 percent in the

post-WWII period, an impressive 4.6% premium over the average bond return of 1.1

percent. Similar statistical differences have been documented for France, Germany, and

Japan. And together, the United States, the United Kingdom, Japan, Germany, and

France account for more than 85 percent of capitalized global equity value.

Table 3 details the equity premium for India for the post liberalization period,

using both the BSE 100 and the Sensex index as a proxy for the return on equity. Since


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participation in the T-bill market was highly regulated before 2000, we report the equity

premium relative to the Bank Deposit Rate, using the later as a proxy for the return on

a risk free security.

For the period prior to 1991 reliable data on dividend yields is not available. In

Table 4, we report the equity premium using the average annual stock price index as

documented and reported by the Reserve Bank of India.

Table 3

India Returns, 1991-2004

Relatively

Riskless

Security

BSE 100

Equity

Premium

(BSE 100)

Sensex

Equity

Premium

(Sensex)

Mean Real

Return % 1.28 12.6 11.3 11.0 9.7Standard

Deviation % 1.73 37.2 37.7 32.6 33.2

Table 4

India Returns, 1984-1991

Relatively

Riskless

Security BSE 100Equity

Premium

(BSE 100)Mean Real

Return % 1.13 22.4 21.3Standard

Deviation % 0.74 28.1 27.9


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We illustrate the dramatic investment implications of the differential rates of

return in Tables 5 and 6. Table 5 shows the enormous disparity in capital appreciation

of $1 invested in different assets in the U.S for various time periods.1Table 6 displays a

similar analysis for India

Table 5.

Real Terminal Value of $1 Invested

Stocks T-Bills Ratio

Investment Period

18892004 $4092.36 $3.14 1,303.30

19262004 $407.56 $1.67 244.051947-2004 $61.70 $1.33 46.39

Table 6.

Real Terminal Value of Rs 1 Invested

Stocks (BSE 100) Bank Deposit Ratio

Investment Period

19842004 Rs 19.25 Rs 1.28 15.04

19912004 Rs 4.68 Rs 1.18 3.97

One can gain additional insights by examining what these differential rates imply

for the time it takes to double ones money. Using rates in India over the 1991-2004

period, the doubling period for investments in stocks is about 6 years compared to about

1The calculations in Table 5 assume that all payments to the underlying asset, such as dividend payments to stocks

and interest payments to bonds, were reinvested and that no taxes were paid.


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55 years for investments in a risk free asset. This kind of long-term perspective

underscores the remarkable wealth-building potential of the equity premium and

highlights why it is of central importance in portfolio allocation decisions, in making

estimates of the cost of capital, and in the current debate about the advantages of

investing Social Security Trust or retirement funds in the stock market.

A Premium for Bearing Risk?

Why has the rate of return on stocks in India and other countries been significantly

higher than the rate of return on relatively risk free assets? An intuitive answer is that

stocks are riskier than bonds and investors require a premium for bearing this

additional risk. Indeed, the standard deviation of the returns to stocks in India (about

30 percent a year historically) is larger than that of the returns to T-bills (about 2

percent a year), so obviously, stocks are considerably riskier than bills.

But are they? Figure 1 illustrates the variability in the annual real rate of return

on the BSE 100 Index while Figure 2 shows the variability of a relatively risk free

security over the 19912004 period.


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To enhance and deepen our understanding of the risk-return trade-off in the

pricing of financial assets, we make a detour into modern asset pricing theory and look

at why different assets yield different rates of return. The deux ex machina of this

theory is that assets are priced such that, ex-ante, the loss in marginal utility incurred

by sacrificing current consumption and buying an asset at a certain price is equal to the

expected gain in marginal utility contingent on the anticipated increase in consumption

when the asset pays off in the future.

The operative emphasis here is the incrementalloss or gainin well being due to

incremental consumption, which must be differentiated from the incremental

consumption itself. This is because the sameamount of incremental consumption may

result in different degrees of well-being at different times. A five-course dinner after a

heavy lunch, for example, yields considerably less satisfaction than a similar dinner

when one is hungry!

As a consequence, assets that pay off when times are good and consumption

levels are high, i.e. when the incremental value of additional consumption is low, are less

desirable than those that pay off an equivalent amount when times are bad and

additional consumption is both desirable and more highly valued.

Let us illustrate this principle in the context of the standard, popular paradigm,

the Capital Asset Pricing Model (CAPM). This model postulates a linear relationship

between an assets beta, a measure of systematic risk, and expected return. Thus, high


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beta stocks yield a high-expected rate of return. That is so because in the CAPM, good

times and bad times are captured by the return on the market. The performance of the

market as captured by a broad based index acts as a surrogate indicator for the relevant

state of the economy. A high beta security tends to pay off more when the market

return is high, that is, when times are good and consumption is plentiful; as discussed

earlier, such a security provides less incremental utility than a security that pays off

when consumption is low, is less valuable to investors and consequently sells for less.

Thus assets that pay off in states of low marginal utility will sell for a lower price than

similar assets that pay off in states of high marginal utility. Since rates of return are

inversely proportional to asset prices, the latter class of assets will, on average, give a

lower rate of return than the former.

Another perspective on asset pricing emphasizes that economic agents prefer to

smooth patterns of consumption over time. Assets that pay off a relatively larger

amount at times when consumption is already high, destabilize these patterns of

consumption, whereas assets that pay off when consumption levels are low, smooth

out consumption. Naturally, the latter are more valuable and thus require a lower rate

of return to induce investors to hold these assets. (Insurance policies are a classic

example of assets that smooth consumption. Individuals willingly purchase and hold

them, in spite of their very low rates of return.)

To return to the original question: are stocks so much more riskier than bills so

as to justify a 7% differential in their rates of return as observed in the U.S?


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What came as a surprise to many economists and researchers in finance was the

conclusion of a research paper that Edward Prescott and I wrote in 1979. Stocks and

bonds pay off in approximately the same states of nature or economic scenarios and

hence, as argued earlier, they should command approximately the same rate of return.

In fact, using standard theory to estimate risk-adjusted returns, we found that stocks in

the U.S on average should command, at most, a 1% return premium over bills. Since,

for as long as we had reliable data, (about a hundred years), the mean premium on

stocks over bills was considerably and consistently higher, we realized that we had a

puzzle on our hands. It took us six more years to convince a skeptical profession and for

our paper The Equity Premium: A Puzzle to be published. (Mehra and Prescott

(1985)).

For the purpose of this article, I have done a similar analysis for India using the

data in Table 6, which contains the sample statistics for the Indian economy for the

19912004 period.

Table 6

Indian Economy Sample Statistics, 19912004Statistic Value

Risk-free rate, Rf 1.0128

Mean return on equity, E(Re) 1.126Mean growth rate of consumption, E(x) 1.0227Standard deviation of growth rate of

consumption, (x) 0.0224Mean equity premium, E(Re) Rf 0.113


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I find that the theoretical equity premium should be in the range 0.02% to 0.16%

if the coefficient of risk aversion is varied from 2 to 10. Since the observed risk premium

in India is an order of magnitude more, we have a puzzle with respect to Indian data as

well.

I want to emphasize that the equity premium puzzle is a quantitativepuzzle.

Standard theory is qualitatively consistent with our notion of risk: stocks do, on

average, return more than bonds in the theoretical model. The puzzle arises from the

fact that the quantitative predictions of the theory are an order of magnitude different

from what has been historically documented. The puzzle cannot be dismissed lightly

because much of our economic intuition and policy directives are based on the very class

of models that fall short so dramatically when confronted with financial data. It

underscores the failure of paradigms central to financial and economic modeling to

capture the characteristic that appears to make stocks comparatively so risky. Hence,

the viability of using this class of models for any quantitative assessmentfor example,

to gauge the welfare implications of alternative stabilization policiesis thrown open to

question.

For this reason, over the past 20 years or so, attempts to resolve the puzzle have

become a major research impetus in finance and economics. Several generalizations of

key features of the MehraPrescott (1985) model have been proposed to reconcile

observations with theory, including alternative assumptions about preferences, modified

probability distributions to admit rare but disastrous events, survivorship bias,


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incomplete markets, and market imperfections. None have satisfactorily resolved the

puzzle.

Recently some researchers and analysts that ex-ante equity premium is likely to

be low. The data used to document the equity premium (over the past 100 years in

some instances) represents as reliable an economic data set as analysts have, and 100

years is long series when it comes to economic data. Before the equity premium is

dismissed, not only do researchers need to understand the observed phenomena, but

they also need a plausible explanation as to why the future is likely to be any different

from the past. Demographic shifts and changes in participation in equity markets will,

of course, impact on the equity premium in India over time. For instance, greater stock

market participation in particular by the younger generation is likely to reduce the

equity premium. However, before these demographic effects play a role, on the basis of

what is currently known, I make the following assertion: the equity premium in the

future is likely to be similar to what it has been in the past and returns to investment in

equity will continue to substantially dominate returns to investment in T-bills for

investors with long planning horizons.

Further Reading:Two introductory articles are Cochrane (1997) and Mehra

(2003). Kocherlakota (1996) and Mehra and Prescott (2003) provide comprehensive

surveys of the literature, while Constantinides (2002) and Mehra (2006) is aimed at

researchers.


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References

Cochrane, J.H. 1997. Where Is the Market Going? Uncertain Facts and Novel

Theories. Economic Perspectives, vol. 21, no. 6 (November):337.

Constantinides G.M. 2002. Rational Asset Prices. Journal of Finance, vol. 57, no. 4

(August):156791.

Kocherlakota, N.R. 1996. The Equity Premium: Its Still a Puzzle. Journal of

Economic Literature, vol. 34, no. 1 (March):4271.

Mehra, R., and E.C. Prescott. 1985. The Equity Premium: A Puzzle. Journal of

Monetary Economics, vol. 15, no. 2 (March):145161.

Mehra, R. 2003. The Equity Premium: Why Is It A Puzzle? Financial Analysts

Journal, January /February, pp 54-69

Mehra, R., and E.C. Prescott. 2003. The Equity Premium in Retrospect. In Handbook

of the Economics of Finance. Edited by G.M. Constantinides, M. Harris, and R. Stulz.

Amsterdam, Netherlands: North-Holland,.

Mehra, R. 2006 Handbook of Investments: Equity Risk PremiumNorth Holland,

Amsterdam (Forthcoming).

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Equity Premium in India